Gday Fraser. Sorry to hear about your bilateral, not a fun experience by any means. Especially for someone in your line of work.
Tennis elbow is sometimes difficult to manage due to the nature of the human body. It is very rare that we allow the extensor tendons in our arm to rest for a prolonged period of time due to their importance. There are some quick tips if you find your elbows flaring up constantly...
1. Ice massage : Ice massage following any aggravating activity can reduce local inflammation and irritation to the extensor tendons and speed up recovery.
2. Light exercise : The trick with tennis elbow is to find the right level of exercise for your current status. The exercise should be painfree and relatively light. The purpose the the exercise you were given was not just to stretch and strengthen your tendons, it was also to desensitise them. After prolonged rest, the muscle and tendons have to get used to performing their old job. It's like you haven't worked out in a year, and you go do a 3 hour gym session with the biggest loser personal trainers. Your muscles need this "warm up" step to properly return to normal. Stopping all exercise at this point is probably not reducing your chronicity but increasing it. If exercise starts to flare up your symtpoms, refer to point 1.
3. Ergonomics! No this is not a economic term, it refers to how you set yourself up at work and what this is doing to your body! Some quick tips...
Take work breaks (5 minute breaks per hour can greatly reduce symptoms)
Raise your chain / lower your desk. You should have a 10-15 degree downward slope of your arms to your desk when typing. This takes stress of your extensor tendons and helps prevent tennis elbow to some degree.
There is probably a lot of other suggestions from the physio community to helping manage tennis elbow in cases such as yours, I'm just a new grad i.e. US / STM / etc. etc. But I am at work so have to run.
As allways, before acting on this information please consult with your current therapist / MD.